Modified MUSIC estimation for correlated signals with compressive sampling arrays

This paper addresses the issue of the direction of arrival （DOA） estimation under the compressive sampling （CS） framework. A novel approach, modified multiple signal classification （MMUSIC） based on the CS array （CSA-MMUSIC）, is proposed to resolve the DOA estimation of correlated signals and two closely adjacent signals. By using two random CS matrices, a large size array is compressed into a small size array, which effectively reduces the number of the front end circuit. The theoretical analysis demonstrates that the proposed approach has the advantages of low computational complexity and hardware structure compared to other MMUSIC approaches. Simulation results show that CSAMMUSIC can possess similar angular resolution as MMUSIC.

Moving object detection in framework of compressive sampling

Compressive sensing is a revolutionary idea proposed recently to achieve much lower sampling rate for signals.In the image application with limited resources the camera data can be stored and processed in compressed form.An algorithm for moving object and region detection in video using a compressive sampling is developed.The algorithm estimates motion information of the moving object and regions in the video from the compressive measurements of the current image and background scene.The algorithm does not perform inverse compressive operation to obtain the actual pixels of the current image nor the estimated background.This leads to a computationally efficient method and a system compared with the existing motion estimation methods.The experimental results show that the sampling rate can reduce to 25% without sacrificing performance.

A METHOD OF IMAGE QUALITY ASSESSMENT FOR COMPRESSIVE SAMPLING VIDEO TRANSMISSION

Based on compressive sampling transmission model, we demonstrate here a method of quality evaluation for the reconstruction images, which is promising for the transmission of unstructured signal with reduced dimension. By this method, the auxiliary information of the recovery image quality is obtained as a feedback to control number of measurements from compressive sampling video stream. Therefore, the number of measurements can be easily derived at the condition of the absence of information sparsity, and the recovery image quality is effectively improved. Theoretical and experimental results show that this algorithm can estimate the quality of images effectively and is in well consistency with the traditional objective evaluation algorithm.

Compressive sampling and reconstruction in shift-invariant spaces associated with the fractional Gabor transform

In this paper,we propose a compressive sampling and reconstruction system based on the shift-invariant space associated with the fractional Gabor transform.With this system,we aim to achieve the subNyquist sampling and accurate reconstruction for chirp-like signals containing time-varying characteristics.Under the proposed scheme,we introduce the fractional Gabor transform to make a stable expansion for signals in the joint time-fractional-frequency domain.Then the compressive sampling and reconstruction system is constructed under the compressive sensing and shift-invariant space theory.We establish the reconstruction model and propose a block multiple response extension of sparse Bayesian learning algorithm to improve the reconstruction effect.The reconstruction error for the proposed system is analyzed.We show that,with considerations of noises and mismatches,the total error is bounded.The effectiveness of the proposed system is verified by numerical experiments.It is shown that our proposed system outperforms the other systems state-of-the-art.

Cramer-Rao bounds for the joint delay-Doppler estimation of compressive sampling pulse-Doppler radar

Time-delay and Doppler shift estimation is a basic task for pulse-Doppler radar processing. For low-rate sampling of echo signals, several kinds of compressive sampling(CS) pulse-Doppler(CSPD) radar are developed with different analog-to-information conversion(AIC) systems. However, a unified metric is absent to evaluate their parameter estimation performance. Towards this end, this paper derives the deterministic Cramer-Rao bound(CRB)for the joint delay-Doppler estimation of CSPD radar to quantitatively analyze the estimate performance. Theoretical results reveal that the CRBs of both time-delays and Doppler shifts are inversely proportional to the received target signal-to-noise ratio(SNR), the number of transmitted pulses and the sampling rate of AIC systems. The main difference is that the CRB of Doppler shifts also lies on the coherent processing interval. Numerical experiments validate these theoretical results. They also show that the structure of the AIC systems has weak influence on the CRBs, which implies that the AIC structures can be flexibly selected for the implementation of CSPD radar.

Compressive sensing based multiuser detector for massive MBM MIMO uplink

Media based modulation(MBM)is expected to be a prominent modulation scheme,which has access to the high data rate by using radio frequency(RF)mirrors and fewer transmit antennas.Associated with multiuser multiple input multiple output(MIMO),the MBM scheme achieves better performance than other conventional multiuser MIMO schemes.In this paper,the massive MIMO uplink is considered and a conjunctive MBM transmission scheme for each user is employed.This conjunctive MBM transmission scheme gathers aggregate MBM signals in multiple continuous time slots,which exploits the structured sparsity of these aggregate MBM signals.Under this kind of scenario,a multiuser detector with low complexity based on the compressive sensing(CS)theory to gain better detection performance is proposed.This detector is developed from the greedy sparse recovery technique compressive sampling matching pursuit(CoSaMP)and exploits not only the inherently distributed sparsity of MBM signals but also the structured sparsity of multiple aggregate MBM signals.By exploiting these sparsity,the proposed CoSaMP based multiuser detector achieves reliable detection with low complexity.Simulation results demonstrate that the proposed CoSaMP based multiuser detector achieves better detection performance compared with the conventional methods.

Adaptive sampling strategy for characterizing spatial distribution of soil liquefaction potential using cone penetration test

Characterizing spatial distribution of soil liquefaction potential is critical for assessing liquefactionrelated hazards(e.g.building damages caused by liquefaction-induced differential settlement).However,in engineering practice,soil liquefaction potential is usually measured at limited locations in a specific site using in situ tests,e.g.cone penetration tests(CPTs),due to the restrictions of time,cost and access to subsurface space.In these cases,liquefaction potential of soil at untested locations requires to be interpreted from limited measured data points using proper interpolation method,leading to remarkable statistical uncertainty in liquefaction assessment.This underlines an important question of how to optimize the locations of CPT soundings and determine the minimum number of CPTs for achieving a target reliability level of liquefaction assessment.To tackle this issue,this study proposes a smart sampling strategy for determining the minimum number of CPTs and their optimal locations in a selfadaptive and data-driven manner.The proposed sampling strategy leverages on information entropy and Bayesian compressive sampling(BCS).Both simulated and real CPT data are used to demonstrate the proposed method.Illustrative examples indicate that the proposed method can adaptively and sequentially select the required number and optimal locations of CPTs.

Compressive Wideband Spectrum Sensing Based on Random Matrix Theory

Spectrum sensing in a wideband regime for cognitive radio network(CRN) faces considerably technical challenge due to the constraints on analog-to-digital converters(ADCs).To solve this problem,an eigenvalue-based compressive wideband spectrum sensing(ECWSS) scheme using random matrix theory(RMT) was proposed in this paper.The ECWSS directly utilized the compressive measurements based on compressive sampling(CS) theory to perform wideband spectrum sensing without requiring signal recovery,which could greatly reduce computational complexity and data acquisition burden.In the ECWSS,to alleviate the communication overhead of secondary user(SU),the sensors around SU carried out compressive sampling at the sub-Nyquist rate instead of SU.Furthermore,the exact probability density function of extreme eigenvalues was used to set the threshold.Theoretical analyses and simulation results show that compared with the existing eigenvalue-based sensing schemes,the ECWSS has much lower computational complexity and cost with no significant detection performance degradation.

Wideband Signal Detection Based on MWC Discrete Compressed Sampling Structure

In order to solve the cross-channel signal problem caused by the uniform channelized wideband digital receiver when processing wideband signal and the problem that the sensitivity of the system greatly decreases when the bandwidth of wideband digital receiver increases,which both decrease the wideband radar signal detection performance,a new wideband digital receiver based on the modulated wideband converter(MWC)discrete compressed sampling structure and an energy detection method based on the new receiver are proposed.Firstly,the proposed receiver utilizes periodic pseudo-random sequences to mix wideband signals with baseband and other sub-bands.Then the mixed signals are low-pass filtered and downsampled to obtain the baseband compressed sampling data,which can increase the sensitivity of the system.Meanwhile,the cross-channel signal will all appear in any subbands,so the cross-channel signal problem can be solved easily by processing the baseband compressed sampling data.Secondly,we establish the signal detection model and formulate the criterion of the energy detection method.And we directly utilize the baseband compressed sampling data to carry out signal detection without signal reconstruction,which decreases the complexity of the algorithm and reduces the computational burden.Finally,simulation experiments demonstrate the effectiveness of the proposed receiver and show that the proposed signal detection method is effective in low signal-to-noise ratio(SNR)compared with the conventional energy detection and the probability of detection increases significantly when SNR increases.

Non-parametric machine learning methods for interpolation of spatially varying non-stationary and non-Gaussian geotechnical properties

Spatial interpolation has been frequently encountered in earth sciences and engineering.A reasonable appraisal of subsurface heterogeneity plays a significant role in planning,risk assessment and decision making for geotechnical practice.Geostatistics is commonly used to interpolate spatially varying properties at un-sampled locations from scatter measurements.However,successful application of classic geostatistical models requires prior characterization of spatial auto-correlation structures,which poses a great challenge for unexperienced engineers,particularly when only limited measurements are available.Data-driven machine learning methods,such as radial basis function network(RBFN),require minimal human intervention and provide effective alternatives for spatial interpolation of non-stationary and non-Gaussian data,particularly when measurements are sparse.Conventional RBFN,however,is direction independent(i.e.isotropic)and cannot quantify prediction uncertainty in spatial interpolation.In this study,an ensemble RBFN method is proposed that not only allows geotechnical anisotropy to be properly incorporated,but also quantifies uncertainty in spatial interpolation.The proposed method is illustrated using numerical examples of cone penetration test(CPT)data,which involve interpolation of a 2D CPT cross-section from limited continuous 1D CPT soundings in the vertical direction.In addition,a comparative study is performed to benchmark the proposed ensemble RBFN with two other non-parametric data-driven approaches,namely,Multiple Point Statistics(MPS)and Bayesian Compressive Sensing(BCS).The results reveal that the proposed ensemble RBFN provides a better estimation of spatial patterns and associated prediction uncertainty at un-sampled locations when a reasonable amount of data is available as input.Moreover,the prediction accuracy of all the three methods improves as the number of measurements increases,and vice versa.It is also found that BCS prediction is less sensitive to the number of measurement data and outperforms RBFN and MPS when only limited point observations are available.

MR IMAGE RECONSTRUCTION BASED ON COMPREHENSIVE SPARSE PRIOR

In this paper, a novel Magnetic Resonance (MR) reconstruction framework which combines image-wise and patch-wise sparse prior is proposed. For addressing, a truncated beta-Bernoulli process is firstly employed to enforce sparsity on overlapping image patches emphasizing local structures. Due to its properties, beta-Bernoulli process can adaptive infer the sparsity (number of non-zero coefficients) of each patch, an appropriate dictionary, and the noise variance simultaneously, which are prerequisite for iterative image reconstruction. Secondly, a General Gaussian Distribution (GGD) prior is introduced to engage image-wise sparsity for wavelet coefficients, which can be then estimated by a threshold denoising algorithm. Finally, MR image is reconstructed by patch-wise estimation, image-wise estimation and under-sampled k-space data with least square data fitting. Experimental results have demonstrated that proposed approach exhibits excellent reconstruction performance. Moreover, if the image is full of similar low-dimensional-structures, proposed algorithm has dramatically improved Peak Signal to Noise Ratio (PSNR) 7～9 dB, with comparisons to other state-of-art compressive sampling methods.

Improved RIP-based bounds for guaranteed performance of two compressed sensing algorithms

Iterative hard thresholding(IHT)and compressive sampling matching pursuit(CoSaMP)are two mainstream compressed sensing algorithms using the hard thresholding operator.The guaranteed performance of the two algorithms for signal recovery was mainly analyzed in terms of the restricted isometry property(RIP)of sensing matrices.At present,the best known bound using the RIP of order 3k for guaranteed performance of IHT(with the unit stepsize)isδ3k<1/√3≈0.5774,and the bound for CoSaMP using the RIP of order 4k isδ4k<0.4782.A fundamental question in this area is whether such theoretical results can be further improved.The purpose of this paper is to affirmatively answer this question and to rigorously show that the abovementioned RIP bound for guaranteed performance of IHT can be significantly improved toδ3k<(√5−1)/2≈0.618,and the bound for CoSaMP can be improved toδ4k<0.5102.

Compression schemes for concept classes induced by three types of discrete undirected graphical models

Sample compression schemes were first proposed by Littlestone and Warmuth in 1986.Undi-rected graphical model is a powerful tool for classification in statistical learning.In this paper,we consider labelled compression schemes for concept classes induced by discrete undirected graphical models.For the undirected graph of two vertices with no edge,where one vertex takes two values and the other vertex can take any finite number of values,we propose an algorithm to establish a labelled compression scheme of size VC dimension of associated concept class.Further,we extend the result to other two types of undirected graphical models and show the existence of labelled compression schemes of size VC dimension for induced concept classes.The work of this paper makes a step forward in solving sample compression problem for concept class induced by a general discrete undirected graphical model.

Stochastic Collocation on Unstructured Multivariate Meshes

Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification(UQ)community.Techniques for leastsquares regularization,compressive sampling recovery,and interpolatory reconstruction are becoming standard tools used in a variety of applications.Selection of a collocation mesh is frequently a challenge,but methods that construct geometrically unstructured collocation meshes have shown great potential due to attractive theoretical properties and direct,simple generation and implementation.We investigate properties of these meshes,presenting stability and accuracy results that can be used as guides for generating stochastic collocation grids in multiple dimensions.